In a wearable device such as a head-mounted display (HMD) device, tracking the positions of the eyes of a user can allow the HMD device to estimate the direction of a user's gaze. Gaze direction can be used as an input to a program that controls the display of images on the HMD. In order to determine the position and gaze of the user's eye, an eye-tracking system may be added to the HMD device. However, developing eye-tracking systems for HMD devices presents a number of technical and practical problems. Eye-tracking systems can add weight, involve large optical components, and require extra processing power. From a user's point of view, the eye-tracking system may create obstructions to the field of view, emit too much light near the user's eye, and cause other optical complications.